Title data
Stoll, Michael:
Chabauty without the MordellWeil group.
In: Böckle, Gebhard ; Decker, Wolfram ; Malle, Gunter
(ed.):
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. 
Cham
: Springer
,
2017
.  pp. 623663
ISBN 9783319705651
DOI: https://doi.org/10.1007/9783319705668_28
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
Based on ideas from recent joint work with Bjorn Poonen, we describe an algorithm that can in certain cases determine the set of rational points on a curve C, given only the pSelmer group S of its Jacobian (or some other abelian variety C maps to) and the image of the pSelmer set of C in S. The method is more likely to succeed when the genus is large, which is when it is usually rather difficult to obtain generators of a finiteindex subgroup of the MordellWeil group, which one would need to apply Chabauty’s method in the usual way. We give some applications, for example to generalized Fermat equations of the form x^5 + y^5 = z^p.
Further data
Item Type:  Article in a book 

Refereed:  Yes 
Keywords:  Rational points on curves; Chabauty’s method; Selmer group 
Subject classification:  Mathematics Subject Classification Code: 11G30 14G05 14G25 14H25 11Y50 11D41 
Institutions of the University:  Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II  Univ.Prof. Dr. Michael Stoll Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  20 Jun 2018 11:29 
Last Modified:  20 Jun 2018 11:29 
URI:  https://eref.unibayreuth.de/id/eprint/44579 